Finite Group Databasebeta

← Group #312243

Character table — Group #312243

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size1111111122222222448888888888888888888888881616161616161616161616161616161632
order12222222444444444444444444444488888888888822444444888888884
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-111-1-1-1-1-1-1111-111-1-111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111-1-111-1-1-1-1-1-1-111111-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111
χ511111111111111111111-1-111-1-1111111-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-11
χ611111111111111111111-1-111-1-111-1-1111111111111-1-11-1-1-1-1-1-1-111-1-111-1
χ711111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-11-1-11111-1-1-1-111-1
χ811111111111111111111-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1111111-1-11
χ9111111111111111111-1-111-1-1111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111
χ10111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111111-1-1-111-1-11111-1-1-1
χ11111111111111111111-1-111-1-111-1-111111111111111-1-1-11-1-1-1-111-1-111-1-1-1
χ12111111111111111111-1-111-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111
χ13111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-11
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-11-1111111-1-11111-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-1111-1-1-1-1111111-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11111-1-1-1-1-1-1-1-11
χ17222222222-22-22-22-2-2-2002200-2-2002200-2-200220000000-20000000000000
χ18222222222-22-22-22-2-2-2002200-2-200-2-2002200-2-2000000020000000000000
χ19222222222-22-22-22-2-2-200-2-200220022002200-2-20000000-20000000000000
χ20222222222-22-22-22-2-2-200-2-2002200-2-200-2-20022000000020000000000000
χ2122222222-22-22-22-22-2-22200-2-20022002200-2-200000000-200000000000000
χ2222222222-22-22-22-22-2-22200-2-200-2-200-2-2002200000000200000000000000
χ2322222222-22-22-22-22-2-2-2-20022002200-2-2002200000000-200000000000000
χ2422222222-22-22-22-22-2-2-2-2002200-2-2002200-2-200000000200000000000000
χ2522-2-2-222-22-2-222-2-22-222i−2i002i−2i0000000000000000002-20000002i−2i0000000
χ2622-2-2-222-22-2-222-2-22-222i−2i002i−2i000000000000000000-22000000−2i2i0000000
χ2722-2-2-222-22-2-222-2-22-22−2i2i00−2i2i0000000000000000002-2000000−2i2i0000000
χ2822-2-2-222-22-2-222-2-22-22−2i2i00−2i2i000000000000000000-220000002i−2i0000000
χ2922-2-2-222-2-222-2-222-2-22002i−2i002i−2i00000000000000000000002-2002i−2i00000
χ3022-2-2-222-2-222-2-222-2-22002i−2i002i−2i0000000000000000000000-2200−2i2i00000
χ3122-2-2-222-2-222-2-222-2-2200−2i2i00−2i2i00000000000000000000002-200−2i2i00000
χ3222-2-2-222-2-222-2-222-2-2200−2i2i00−2i2i0000000000000000000000-22002i−2i00000
χ3322-2-2-222-2-2-222-2-2222-22i−2i2i−2i−2i2i−2i2i000000000000000000002-200000000000
χ3422-2-2-222-2-2-222-2-2222-22i−2i−2i2i−2i2i2i−2i00000000000000000000-2200000000000
χ3522-2-2-222-2-2-222-2-2222-2−2i2i2i−2i2i−2i−2i2i00000000000000000000-2200000000000
χ3622-2-2-222-2-2-222-2-2222-2−2i2i−2i2i2i−2i2i−2i000000000000000000002-200000000000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ38444-4-4-4-4400000000000000000000002i2−2i222−2200002i2i−2i−2i00000000000000000
χ39444-4-4-4-4400000000000000000000002i2−2i2−22220000−2i−2i2i2i00000000000000000
χ40444-4-4-4-440000000000000000000000−2i22i222−220000−2i−2i2i2i00000000000000000
χ41444-4-4-4-440000000000000000000000−2i22i2−222200002i2i−2i−2i00000000000000000
χ4244-4-4-444-444-4-444-4-44-400000000000000000000000000000000000000000
χ434-444-44-4-4040-40-40400000000004i−4i0000000000000000000000000000000
χ444-444-44-4-4040-40-4040000000000−4i4i0000000000000000000000000000000
χ454-444-44-4-40-404040-400000000000000000000000000000000000000002i2−2i20
χ464-444-44-4-40-404040-40000000000000000000000000000000000000000−2i22i20
χ474-44-44-44-440-40-4040000000000000000000000000000000000000002i2−2i2000
χ484-44-44-44-440-40-404000000000000000000000000000000000000000−2i22i2000
χ494-44-44-44-4-404040-400000000000004i−4i00000000000000000000000000000
χ504-44-44-44-4-404040-40000000000000−4i4i00000000000000000000000000000
χ514-4-44-4-4444040-40-40000000000000000000004i−4i000000000000000000000
χ524-4-44-4-4444040-40-4000000000000000000000−4i4i000000000000000000000
χ534-4-44-4-444-40-404040000000000000000000000022−2222−2200000000000000000
χ544-4-44-4-444-40-4040400000000000000000000000−2222−222200000000000000000
χ554-4-4-444-4404040-40-400000000000000000000002i2−2i2−2i22i200000000000000000
χ564-4-4-444-4404040-40-40000000000000000000000−2i22i22i2−2i200000000000000000
χ574-4-4-444-440-40-404040000000000000000004-400000000000000000000000
χ584-4-4-444-440-40-40404000000000000000000-4400000000000000000000000
χ5988-888-8-8-8000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).